While all of this may seem suspect to some readers, we would like to stress that these are very standard constructions. Alternatively stated, all of what has been mentioned so far are the standard mathematical techniques used to study these spaces and can be found in any textbook (cf. [1]}, [2]}). Here we are bringing out the full physical significance of these mathematical constructs, which is too often overlooked. Understanding the link between the mathematical structures and the physics they represent is crucial to clearing out possible misunderstandings.
